Image quality assessments (IQA) are an important task for providing appropriate medical care. Full-reference IQA (FR-IQA) methods, such as peak signal-to-noise ratio (PSNR) and structural similarity (SSIM), are often used to evaluate imaging conditions, reconstruction conditions, and image processing algorithms, including noise reduction and super-resolution technology. However, these IQA methods may be inapplicable for medical images because they were designed for natural images. Therefore, this study aimed to investigate the correlation between objective assessment by some FR-IQA methods and human subjective assessment for computed tomography (CT) images. For evaluation, 210 distorted images were created from six original images using two types of degradation: noise and blur. We employed nine widely used FR-IQA methods for natural images: PSNR, SSIM, feature similarity (FSIM), information fidelity criterion (IFC), visual information fidelity (VIF), noise quality measure (NQM), visual signal-to-noise ratio (VSNR), multi-scale SSIM (MSSSIM), and information content-weighted SSIM (IWSSIM). Six observers performed subjective assessments using the double stimulus continuous quality scale (DSCQS) method. The performance of IQA methods was quantified using Pearson’s linear correlation coefficient (PLCC), Spearman rank order correlation coefficient (SROCC), and root-mean-square error (RMSE). Nine FR-IQA methods developed for natural images were all strongly correlated with the subjective assessment (PLCC and SROCC > 0.8), indicating that these methods can apply to CT images. Particularly, VIF had the best values for all three items, PLCC, SROCC, and RMSE. These results suggest that VIF provides the most accurate alternative measure to subjective assessments for CT images.